1. Introduction

Dense urbanisation has decoupled urban dwellers from natural ecosystems, consequently diminishing human health, environmental quality and equitable socio-economic progess (Tzoulas., 2007). Green infrastructure (GI) integration emerged as an effective practice for generating urban ecosystem services including carbon sequestration, micro-climate control, environmental purification and human well-being (Lovell and Taylor, 2013). However, incorporating GI in dense urban agglomorations persists to be a significant challenge. Green roofs (GR) consist of a vegetation layer, a substrate layer and a drainage layer installed on a building roof (Mentens, 2006). Ecosystem benefits of GRs include air purification, storm-water retention, temperature regulation, water purification, increased urban bio-diversity and building energy efficiency (Oberndorfer et al., 2007). Furthermore, GI can improve public health and mental well-being for those who have suffucient access to it (Wolch et al., 2014). The aim of this mini-project is to propose a GIS-based Multi-crirteria Decision Analysis tool (GreenRoof Tool) that optimizes GR ecosystem benefits in London.

2. Methodology

GIS-based Multi-criteria Decision Analysis (GIS-MCDA) has become a widely employed practice in site-suitability analysis for land-use projects that involve complex and often opposing factors (Malczewski, 2006). GIS-MCDA involves step-by-step procedures with geographical criteria data, data manipulation and decision-maker’s preferences to select optimal sites according to a pre-defined objective (Drobne and Lisec, 2009). The following sub-sections will dicuss how the procedures were implemented for GreenRoof Tool.

2.1 Objective Definition

The first step of GIS-MCDA is to set an objective that defines evaluation criteria and their decision rules (Drobne and Lisec, 2009). The Mayor of London has set a target to transform London into a National Park City, where more than half of urban area is green space (GLA, 2018a). GRs can effectively promote GI in London, however the locality of GRs is essential in optimising ecosystem services (Gwak et al., 2017). The objective of this GIS-MCDA is to identify locations that optimise GR performance regarding major sustainability challenges in London.

2.2 Selecting Evaluation Criteria

Evaluation criteria, or ‘attributes’, are objective functions that reflect concerns of decision-makers with regards to optimising the success of a development (Drobne and Lisec, 2009). Gwak et al. (2017) imply that GR evaluation criteria should reflect the variable spatial conditions in a city. Spatial environmental, social and economic phenomena will form GreenRoof Tool’s evaluation criteria. Commonly stated ecosystem services of GRs include storm-water management, air purification, temperature regulation, property value rise and improved human health (Getter and Rowe, 2006; Bianchini and Hewage, 2012). Roof size also influences benefit per unit area that a GR can provide (Gwak et al., 2017). Based on academic evidence and available spatial data, nine evaluation criteria were selected for this analysis:

  • Roof size (m^2)
  • Nitrogen Dioxide Concentration
  • Particulate Matter 2.5 Concentration
  • Flood Risk Zones
  • Urban Heat Island Data
  • Life Expectancy - ward level
  • Access to Green Space - ward level
  • Subjective Happiness (Well-being) Score - ward level
  • Median House Price - ward level

2.3 Data Collection and Manipulation

Buildings - https://www.ordnancesurvey.co.uk/opendatadownload/products.html

Shapefile of Buildings within the TQ National Grid Reference Square from OS Open Map - Local. The building layer required preliminary clipping to the London shapefile boundary. Area (m^2) of each building was calculated using st_area().

Figure 1. Building Roofs in London

Figure 1. Building Roofs in London

London Wards - https://data.london.gov.uk/dataset/statistical-gis-boundary-files-london

Shapefile of London wards used to clip the buildings layer and spatially join well-being scores and house price data.

Figure 2. London Wards

Figure 2. London Wards

Urban Heat Island Map - https://data.london.gov.uk/dataset/london-s-urban-heat-island

Average of the maximum daily temperatures (WSAVGMAX Column) during Summer 2006 in 1 km by 1km grid resolution to measure urban heat island effect in London. Areas with higher summer temperatures will have a higher suitability index, as green roofs would help reduce temperatures in these areas.

Figure 3. Urban Heat Island Map in London

Figure 3. Urban Heat Island Map in London

Air Quality Data - https://data.london.gov.uk/dataset/london-atmospheric-emissions-inventory-2013

NO2 and PM2.5 are established as the deadliest air pollutants in London (London Councils, 2018). Raster 20 m grid data on NO2 and PM2.5 concentration modelled for 2020 (2013 base-year) was employed.

Figure 4. Modelled NO2 concentration (2020) in London

Figure 4. Modelled NO2 concentration (2020) in London

Figure 5. Modelled PM2.5 concentration (2020) in London

Figure 5. Modelled PM2.5 concentration (2020) in London

Flood Risk Zones - https://data.london.gov.uk/dataset/flood-risk-zones

Shapefile indicating probability of flood risk (High, Medium, Low and Very Low) flood risk in London for 2017. Preliminary numeric conversions of the categorical was performed:

  • High = 4
  • Medium = 3
  • Low = 2
  • Very Low = 1
#Numerising Flood Risk Scores from PROB_4BAND Column

i <- 0

for (i in 1:nrow(FloodRiskSF)){
  
  if(FloodRiskSF$PROB_4BAND[i] == "High"){
    
    FloodRiskSF$SCORE[i] <- 4
    
  } else if (FloodRiskSF$PROB_4BAND[i] == "Medium"){
    
    FloodRiskSF$SCORE[i] <- 3
    
  } else if (FloodRiskSF$PROB_4BAND[i] == "Low"){
    
    FloodRiskSF$SCORE[i] <- 2
    
  } else if (FloodRiskSF$PROB_4BAND[i] == "Very Low"){
    
    FloodRiskSF$SCORE[i] <- 1
    
  }
  
}
Figure 5. London Flood Risk Zones.

Figure 5. London Flood Risk Zones.

Well Being Scores - https://data.london.gov.uk/dataset/london-ward-well-being-scores

Well-being scores for London Wards, Scores above zero indicate that inhabitants of a ward are more likely to experience higher well-being and vice versa. Life Expectancy, Access to Green Space and Subjective Happiness scores were employed in the analysis (Figures 6-8).

Figure 6. Life Expectancy Score of London Wards.

Figure 6. Life Expectancy Score of London Wards.

Figure 7. Access to Green Space Scores of London Wards

Figure 7. Access to Green Space Scores of London Wards

Figure 8. Subjective Happiness Scores of London Wards.

Figure 8. Subjective Happiness Scores of London Wards.

Median House Price by Ward - https://data.london.gov.uk/dataset/average-house-prices

Median House Value (2017) within London Wards. Bianchini and Hewage (2012) suggested that GR installation can increase property value by up to $648/m2. Areas with lower property values were prioritized in the tool.

Figure 9. Median House Price (2017) of London Wards.

Figure 9. Median House Price (2017) of London Wards.

2.4 Data Standardization

To compare datasets measured on different scales, Boolean or Fuzzy logic are typically implemented in GIS-MCDA data standardization. Boolean logic ascertains a definite ‘cut-off point’, with only two outcomes; true(1) or false(0) (Otgonbayar et al., 2017). Fuzzy logic places observations on a continuum of grades of membership from 0 to 1 to accommodate for situations of uncertainty (Zadeh, 1965). When decision-makers are uncertain about site suitability in GIS-MCDA, Jiang and Eastman (2000) imply fuzzy logic is useful. Fuzzy logic was utilized in the analysis, due to uncertainty on optimal GR locations in London. A simple min-max scaling equation was employed for data standardization (Zadeh, 1967).

Equation 1. Min-max Fuzzy Scaling Equation (Zadeh, 1967)

Equation 1. Min-max Fuzzy Scaling Equation (Zadeh, 1967)

Fuzzy Functions

The ‘FuzzScale’ function was developed based on Equation 1 (Function 1).‘RastFuzzScale’ implements Equation 1 for raster layers (Function 2). ‘InverseFuzz’ inverses fuzzy data for well-being scores and house prices, enabling prioritization for areas with lower life expectancy, for example.

Function 1. Fuzzy Linear Scaling Function for vector dataframes.

#FuzzScale accepts an "input" dataframe and a "header" to specify the column to the apply scaling to. The function returns a new column named "FUZZ_SCALE" with the values rescaled from 0-1. 
FuzzScale <- function(input, header){
  
  
  attach(input)
  
  FUZZ_SCALE <- header
  
  MN <- min(FUZZ_SCALE)
  MX <- max(FUZZ_SCALE)
  
  print(MN)
  print(MX)
  
  i <- 0
  
  for (i in 1:nrow(input)){
    
    FUZZ_SCALE[i] <- (FUZZ_SCALE[i]-MN)/(MX-MN)
    
  }
  
  
 return(input <- cbind(input, FUZZ_SCALE))
  
}

Function 2. Fuzzy Linear Scaling Function for raster data.

#FuzzScale accepts a "raster" file and returns re-scaled values (0-1) of the layer.

RastFuzzScale <- function(raster){
  
  raster <- setMinMax(raster)
  
  min <- minValue(raster)
  max <- maxValue(raster)
  
  return(raster <- (raster - min)/(max-min))
  
}

Function 3. Inverse Fuzzy Scaling Function.

#InverseFuzz takes an "input" data frame and inverses the FUZZ_SCALE column.

InverseFuzz <- function(input){
  
  
  FUZZ_SCALE <- input$FUZZ_SCALE
  
  input$FUZZ_SCALE <- NULL
  
  i <- 0
  
  for(i in 1:nrow(input)){
    
    FUZZ_SCALE[i] <- 1 - FUZZ_SCALE[i]
    
  }
  
  return(input <- cbind(input, FUZZ_SCALE))
}

2.5 Analytical Hierarchical Process (AHP)

The Analytical Hierarchical Process (AHP) is an adoption of Weighted Linear Combination (WLC) used to derive weights for criteria layers and aggregating them to attain a suitability index (Drobne and Lisec, 2009). Each attribute is compared to one another using a preference matrix and Saaty’s pairwise comparison scale (Table 1) (Mu and Rojas, 2017). Criteria weightings for this study were based on primary sustainability issues within GLA strategy documentation. Criteria considered to be equally important were given the same ranking.

Table 1. Saaty’s Pairwise Comparison Scale (Saaty, 1980)
Verbal.Judgement Numeric.Value
Extremely Important 9
8
Very Strongly More Important 7
6
Strongly More Important 5
4
Moderetaly More Important 3
2
Equally Important 1

2.6 Criteria Ranking

Air pollution was deemed “the most pressing environmental threat to the future health of London”, with 9,000 Londoners dying sooner than they should due to toxic air quality (GLA, 2018a). NO2 and PM2.5 were ranked at 9. GLA’s environment strategy highlights that London’s flood risk is likely to increase in the future as climate change will induce heavier rainfall and high magnitude storms (GLA, 2018a). A significant future threat, it was ranked 7. Another consequence of future global warming, heat risk is likely to make homes, workplaces and public transport “uncomfortable for all and dangerous for the most disadvantaged” (GLA, 2018a). It was ranked 5, since air pollution and flooding risks more lives.

In social aspects, London experiences vast socio-economic inqualities, has the greatest gap in life expectancy between local authorities relative to other English cities, highlighting London’s vast socio-economic inqeualities (GLA, 2018b). Life expectancy was ranked 7 as green roofs can potentially alleviate inqualities by promoting cleaner air and improving quality of life for unhealthy citizens (Oberndorfer, 2007). Public Health England (2014) pointed out that inqeual access to green spaces amongst neighborhoods contributes to health inqualities in London, ranked at 5. Improving mental health and well-being in London has become a prominent objective within the GLA’s Health Inqualities Strategy (GLA, 2018b), hence ranked 5. Economic aspects of this analysis are captured by median house price within London Wards during 2017. GLA highlighted that wealth inqualities in London were exacerbated as property values increased at a faster rate in affluent neighborhoods (GLA, 2017). Alleviating inqualities is vital for London’s economic development, however don’t threaten human lives as do climate change, environmental pollution and diminished pubic health, therefore ranked at 3. Lastly, larger roof sizes will maximize green roof performance, thus ranking this criteria at 7. Based on literature review, derived criteria rankings are shown in Table 2.

The CriteriaWeighting( ) function has been developed to generate weightings for each criteria, adopting the AHP preference matrix methodology from Mu and Rojas (2017). The function takes a dataframe as shown in Table 2, then generates a weighting of each criteria using a pairwise preference matrix (Function 4).

Function 4. Criteria Weighting Function

#Two column dataframe of criteria dataframe names and their rankings
Rankings <- data.frame(cbind(Criteria = c('BuildingSF', 'HeatMapSF', 'FloodRiskSF', 'NO2_Stdz', 'PM2.5_Stdz', 'LifeExp_Wards', 'GreenAcc_Wards', 'Happiness_Wards', 'HousePrice_Wards'), Rankings = c(7, 7, 9, 9, 9, 7, 5, 5, 3)))


CriteriaWeighting <- function(CriteriaRanking){

  
  #Build a preference matrix using criteria names as row and column names, generating a pairwise matrix.
  PreferenceMatrix <- data.frame(matrix(data = 0, nrow = length(CriteriaRanking[,1]), ncol = length(CriteriaRanking[,1])))
  colnames(PreferenceMatrix) <- CriteriaRanking[,1]
  rownames(PreferenceMatrix) <- CriteriaRanking[,1]
  
  #Calculate difference between rankings of each pairwise criteria to attain their relative importance.
  #Criteria with the same rankings will attain a score of 1
  #Criteria that is lower compared to its pairwise counter-part is reciprocated by their difference in rank. 
  i <- 0
  j <- 0
  k <- 0
  l <- 0
  
  for(i in 1:nrow(PreferenceMatrix)){
  
  for(j in 1:ncol(PreferenceMatrix)){
    
    for(k in 1:nrow(CriteriaRanking)){
      
      for(l in 1:nrow(CriteriaRanking)){
        
        if(rownames(PreferenceMatrix[i,]) == as.character(CriteriaRanking[k,1]) & colnames(PreferenceMatrix[j]) == as.character(CriteriaRanking[l,1])){
          
          if(as.numeric(as.character(CriteriaRanking[k,2])) < as.numeric(as.character(CriteriaRanking[l,2]))){
            
            PreferenceMatrix[i,j] <- 1 / ((as.numeric(as.character(CriteriaRanking[k,2])) - as.numeric(as.character(CriteriaRanking[l,2]))) * -1)
          
          } else if (as.numeric(as.character(CriteriaRanking[k,2])) == as.numeric(as.character(CriteriaRanking[l,2]))){
            
            PreferenceMatrix[i,j] <-  1
            
          } else if(as.numeric(as.character(CriteriaRanking[k,2])) > as.numeric(as.character(CriteriaRanking[l,2]))){
          
            PreferenceMatrix[i, j] <- as.numeric(as.character(CriteriaRanking[k,2])) - as.numeric(as.character(CriteriaRanking[l,2]))
          
          }
          
          }
            
        }
    
      }
  }
 
  }

 Total <- PreferenceMatrix[,1]
  
  #Normalising each matrix observation by the sum of its column
 
 s <- 0
 i <- 0
 j <- 0
 
  for(s in 1:ncol(PreferenceMatrix)){
    
    Total[s] <- sum(PreferenceMatrix[,s])
    
  }
  
  for(i in 1:nrow(PreferenceMatrix)){
    
    for(j in 1:ncol(PreferenceMatrix)){
    
      PreferenceMatrix[i,j] <- PreferenceMatrix[i,j]/Total[j]
    
    }
  }
  

  
  #Averaging each row and putting it in a new column (Weight) to obtain the weighted average of the criteria.
 i <- 0
 
  for(i in 1:nrow(PreferenceMatrix)){
  
    PreferenceMatrix$Weight[i] <- rowMeans(PreferenceMatrix[i,1:9])
 
  }
  
  Weightings <- CriteriaRanking
  Weightings$Rankings <- NULL
  Weightings$Weight <- PreferenceMatrix$Weight
  
  
  return(Weightings)
  
}
  

Criteria_Weights <- CriteriaWeighting(Rankings)
Table 2. Weighted Average of each criteria
Criteria Weight
Roof Size 0.0991570
Urban Heat Island 0.0991570
Flood Risk 0.1919648
Nitrogen Dioxide 0.1919648
Particulate Matter 2.5 0.1919648
Life Expectancy 0.0991570
Access to Green Space 0.0495785
Happiness Score 0.0495785
House Price 0.0274774

2.7 Applying Weights to Criteria Layers

Weighted scores for each criteria is obtained by multiplying each observation by its weighted average, as shown by Function 5 and 6.

Function 5. Critera weighting application for vector layers.

#WeightedScore( ) takes a criteria dataframe and a table of weighted average scores generated by CriteriaWeighting( ), the function identifies the input critera's name within the weighted averages table and applies its respective weighted average to the standardized fuzzy objects within the dataframe.

WeightedScore <- function (input, weightMatrix){
  
  i <- 0
  
  x <- deparse(substitute(input))
  
  Weighted_Score <- input$FUZZ_SCALE
  
  W <- weightMatrix$Weight[weightMatrix$Criteria == x]
  
  for(i in 1:nrow(input)){
      
    Weighted_Score[i] <- Weighted_Score[i] * W
    
  }
  
  return(input <- cbind(input, Weighted_Score))
  
}

Function 6. Criteria weighting application for raster layers.

##RastWeightedScore applies weighted average for raster layers (NO2 and PM2.5)

RastWeightedScore <- function (input, weightMatrix){
  
  inputCriteria <- deparse(substitute(input))
  
  W <- weightMatrix$Weight[weightMatrix$Criteria == inputCriteria]
  
  return(input <- input * W)
  
}

2.8 Rasterizing Criteria Layers

Processed polygon layers were rasterized using the ‘Fasterize’ package (Figure 10). NO2 served as a template raster for fasterize( ).

##Example - Building polygon to Raster using fasterize, NO2 used as raster template.

Buildings_Raster <- fasterize(BuildingSF, NO2, field = "Weighted_Score", fun = "sum", background = NA)

Figure 10. Rasterized Weighted Criteria layers

2.9 Layer Aggregation

Raster layers were aggregated by summing weighted average scores, using overlay().

##Stack All Raster Layers

SuitabilityMap <- overlay(Buildings_Raster, Heat_Raster, Flood_Raster, LE_Raster, GSA_Raster, Happiness_Raster, HousePrice_Raster, NO2_Stdz, PM2.5_Stdz, fun = sum)

3. Results

Figure 11. GreenRoof Tool Final Output. PLEASE VIEW Figure11_FinalOutput.html IN ZIP FILE FOR FULL DETAIL

Full-Extent

Full-Extent

Mid-range Extent

Mid-range Extent

Close Extent

Close Extent

4. Discussion and Limitations

GreenRoof Tool has generated a cellular representation of building roofs in London colored by suitability index according to aggregated weighted criteria. High resolution of the output map provides a detailed visualization where roofs of high suitability can be identified with sufficient spatial accuracy, enabling users to effectively pin-point locations suited to their criteria scores. Datasets employed for this analysis provide insight on spatial conditions where green roofs’ social, economic and environmental performance can be optimized, which can holistically support urban planning policies. Application of fuzzy logic produced ‘suitability’ grades, which can reveal ‘parcels’ of GR optimality. Custom-built functions facilitated efficient data standardization, generating criteria weights and weight application for both vector and raster layers. With further adjustments, these functions could be used for data from other cities, following necessary data manipulation. AHP enabled user selection of weightings with Saaty’s Pairwise Comparison Scale and effective weight derivation for criteria. User input can generate biased weightings, which is a drawback of AHP. A literature review on respective criteria was conducted to minimize bias, thus it is important that criteria weightings are supported by scientific evidence and reflect public concerns if used in a planning context.

Suitability index purely quantifies potential green roof optimization according to weighted criteria. It is important to note that it does not provide statistical evidence of the “best” location. GIS-MCDA serves as an aid in the decision-making process, not a definitive outcome (Drobne and Lisec, 2009). Outcomes of GreenRoof Tool are subject to the user’s intepretation, expertise, knowledge and their weighting preferences. Another important note is that criteria weightings are likely to vary with study area, implementing this analysis for another city will require a deep understanding of literature on local sustainability issues. Roof slope and GR type were not accounted for in this tool, a signficant limitation. “Intensive Green Roofs” require a flat roof, while “Extensive Green Roofs” can be built on sloped roofs (Getter and Rowe, 2006). Incorporating roof slope using LiDAR data, building type and additional criteria for green roof typologies would improve GreenRoof Tool’s applicability.

5. Future Considerations

GreenRoof Tool can be developed in the future by integrating a post-hoc analysis for optimized site-selection. For example, suitable locations have been identified, potential environmental, social and economic benefits can be quantified. Cost-benefit analysis for green roofs have gained academic interest, these techniques can be integrated into the GreenRoof Tool (Bianchini and Hewage, 2012; Gwak et al., 2017). Including flora species would add further depth, Lundholm et al. (2011) revealed that green roof performance is dependent on the type, diversity and richness of its species. Specific criteria weightings can be given to species based on their primary ecosystem functions, generating higher performance.

6. Conclusion

GreenRoof Tool can serve as a preliminary multi-criteria function to the decision-making process for green-roof site-selection. The tool enables a holistic spatial evaluation of green roof ecosystem benefits across all three dimensions of sustainable development in an urban context. Further developments such as incorporating green roof type, plant species, LiDAR data and post-hoc cost-benefit analysis can produce a sophisticated analysis for further optimizing ecosystem services of green roofs. Such a tool can aid municipal authorities effectively pursue urban green infrastructure policies, such as London’s ambition to be a National Park City.

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